Confused

You manage a cable TV franchise in a cluster of Toronto suburbs. With the industry having been deregulated, you have the freedom to set basic cable subscription rates in your area, where you are the only provider. Using your own historical cost records, you have estimated the following monthly total cost function for your franchise: TC = 140, 000 + 5Q + 0.0002Q2 where TC is total cost ($/month) and Q is output measured in subscribers per month. Using information from a demand study conducted by a trade association, you have con- structed the following demand and inverse demand functions for basic cable subscriptions: Demand function: Q = 60, 000 - 2, 500P Inverse demand function: P - 24 - 0.0004Q Once again, Q is the number of households subscribing to your service and P is the monthly fee for a basic subscription. 1. (8 points) Write an algebraic expression for the monthly profit function for this fran- chise (4 points). Then find the profit maximizing number of subscriptions (4 points). (Show your calculations. Show both FOC and SOC). 2. (4 points) What is the monthly subscription fee the firm will charge in order to achieve the profit maximizing number of subscriptions? (Show your calculations.)